Fractions (OCR GCSE Maths: Higher): Exam Questions

Work out 

Give your answer as a mixed number in its simplest form.

Work out 

Work out 

Work out 

Give your answer as a mixed number in its simplest form.

Work out  
Give your answer as a mixed number in its simplest form.

In a school,  of the students study a language.

Of those students who study a language,  study Spanish.

Find the ratio of students who study Spanish to students who do not study Spanish.

A unit fraction has a numerator equal to 1, for example  and .

Unit fractions can be written as the sum of two different unit fractions, for example

Write each of the following unit fractions as the sum of two different unit fractions.

Show that  

Show that   

Show that  

Show that 

Show that   

Show that 

A book has 320 pages.

On Monday, Maya read of the book.

On Tuesday, she read of the book.

Maya read no more of the book.

Find how many pages of the book Maya has left to read.

Show that 

The range of a set of numbers is 
The smallest number is 

Work out the largest number.

Circle the number half way between   and 

Work out the value of  

Circle your answer.

Work out 

Give your answer as a mixed number.

Work out  

Give your answer as a mixed number in its simplest form.

Work out 

Give your answer as a mixed number in its simplest form.

Write the numbers 3, 4, 5 and 6 in the boxes to give the greatest possible total.

You may write each number only once.

Charlie and Jasmine share cartons of apple juice.

Charlie drinks  of a carton every day.

Jasmine drinks  of a carton every day.

Any apple juice left in a carton at the end of the day is used the following day.

The cost of a carton is 70p.
Charlie and Jasmine buy just enough cartons to last them for 10 days.

How much do they spend in total for these cartons? Give your answer in £.
Show your working.

£ ..........................................................

Mrs Mills buys 4 packs of treats for her cats, Fluff and Tigger.
She gives Fluff  of a pack each day.

She gives Tigger  of a pack each day.

For how many complete days will the 4 packs of treats last?

Sally has 30 feet of ribbon.

She cuts strips each of length   feet from the ribbon.

Sally says

      I can cut 13 of these strips from this ribbon.

Is she correct?
Show how you decide.

Show that 

There are  children in a club.

In the club, the ratio of the number of girls to the number of boys is 

of the girls play a musical instrument.

of the boys play a musical instrument.

What fraction of the  children play a musical instrument?

Show that 

Each month Edna spends all her income on rent, on travel and on other living expenses.

She spends  of her income on rent.

She spends  of her income on travel.

She spends  of her income on other living expenses.

Work out her income each month.

A shopkeeper compares the income from sales of a laptop in March and April.

April

By what fraction does the income from these sales decrease in April?

A ball is thrown from a height of 15 metres.

It bounces to height , then to height  as shown.

 is three quarters of the original height.

Jack expects  to be three quarters of 

Work out the value of  that he expects.

.........................metres

In fact,  is two thirds of 

How does this affect the answer to part (a)? Tick a box.

     The ball bounced higher than he expected

       The ball bounced lower than he expected

Show working to support your answer.

In an office there are twice as many females as males.

 of the females wear glasses.

  of the males wear glasses.

84 people in the office wear glasses.

Work out the number of people in the office.